Write the equation of the circle with center (-3,2) and (6,4) a point on the circle

(x + 3)² + (y - 2)² = 85

the equation of a circle in standard form is

(x - a)² + (y - b)² = r²

where (a, b ) are the coordinates of the centre and r is the radius

the radius is the distance from the centre to the point (6, 4 ) on the circle

r = √(x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 3, 2 ) and (x₂, y₂ ) = (6, 4 )

r = √(6 + 3 )² + (4 - 2 )² = √(81 + 4 ) = √85 ⇒ r² = 85

(x + 3)² + (y - 2)² = 85 ← equation of circle